Given that we now know that Winter is fighting to keep the Outsiders beyond the Outer Gates---and Mother Winter, the most powerful creature of Winter, has apparently been injured by the loss of her "walking stick"---the theft of the Blackstaff takes on some interesting (and rather sinister) implications (if in fact the Blackstaff belongs to Mother Winter). Without the Blackstaff, Mother Winter apparently cannot physically take part in the battle at the Gates, as Mother Summer says Mother Winter almost never leaves her cottage. It seems like the loss of the Blackstaff crippled (in large part) the battle capabilities of Winter's most powerful agent (hard to do battle when you can't get yourself to the battlefield), which is something the Nemesis would presumably want very, very much.
So I wonder if the Nemesis, or some Outsider-friendly force in general, orchestrated the theft of Mother Winter's "walking stick"? That would mean that the Winter Queens have been targets for quite a while (I don't think we've ever been told exactly when the Blackstaff first came into the White Council's possession). And it makes quite a bit of strategic sense: first you cripple the most powerful Queen, then you go after the weakest Queen, leaving the Queen in the middle (Mab), the one actually in charge of the troops, incapable of calling for backup when you finally turn your attention to her.
Rashid doesn't actually say that the Senior Council in general (or Ebenezer in particular) know about the Winter Court/Outer Gates situation---he says the Council "knows only as much about our roles as it needs to---and that isn't much." There's no guarantee that the White Council has any idea of the implications of taking the Blackstaff away from Mother Winter. Knowing about Demonreach isn't the same thing as knowing about the Winter Court's actual purpose. And though I presume Mother Winter knows the Council has her staff, it's entirely possible that nobody mentioned the origins of the Blackstaff to Rashid himself, which would explain why he doesn't try to unilaterally get it back from Ebenezer; between wizards' penchants for secrecy and the Winter Queens' oft-mentioned pride, this might be a situation where people aren't sharing information (Mother Winter doesn't tell anyone what happened to the Blackstaff because it hurts her pride to ask for help, Rashid doesn't unilaterally get the Blackstaff back for her because nobody's ever told him what it really is), thus playing into the Nemesis's hands. And even if Rashid does know, he might not be able to get the Blackstaff away from Ebenezer without letting the Council know more about what's going on than apparently he wants them to know.